Density hybrid functionals

The HE, GVB, local MP2, and DFT methods are available, as well as local, gradient-corrected, and hybrid density functionals. The GVB-RCI (restricted configuration interaction) method is available to give correlation and correct bond dissociation with a minimum amount of CPU time. There is also a GVB-DFT calculation available, which is a GVB-SCF calculation with a post-SCF DFT calculation. In addition, GVB-MP2 calculations are possible. Geometry optimizations can be performed with constraints. Both quasi-Newton and QST transition structure finding algorithms are available, as well as the SCRF solvation method. 

Orlova et al. (2003) theoretically studied the mechanism of the firefly bioluminescence reaction on the basis of the hybrid density functional theory. According to their conclusion, changes in the color of light emission by rotating the two rings on the 2-2 axis is unlikely, whereas the participation of the enol-forms of oxyluciferin in bioluminescence is plausible but not essential to explain the multicolor emission. They predicted that the color of the bioluminescence depends on the polarization of the oxyluciferin molecule (at its OH and O-termini) in the microenvironment of the luciferase active site the... 

Hybrid density functional calculations have been carried out for AU-O2, Au-CO, Aui3, AU13-O2, Au -CO, AU13-H2, and AU55 clusters to discuss the catalytic behavior of Au clusters with different sizes and structures for CO oxidation [179]. From these calculations, it was found that O2 and CO could adsorb onto several Au model systems. Especially, icosahedral Aun cluster has a relatively weak interaction with O2 while both icosahedral and cubooctahedral Aui3 clusters have interactions with CO. These findings suggest that the surfaces of the Au clusters are the active sites for the catalytic reactions on the supported and unsupported Au catalysts. 

Two possible routes are envisioned for X = B in Scheme 7-21. The authors favored a path involving the oxidative addition of the S-B bond to Pd(0), insertion of the alkyne into the Pd-S bond followed by C-B bond-forming reductive elimination. On the other hand, Morokuma et al. studied the mechanism of the addition of HSB(0CH2)2 (99) to acetylene (C2H2) using Pd(PH3)2 (100) as a catalyst to produce 101 using hybrid density functional calculations (Eq. 7.62) [5]. 

Zhao, Y. Lynch, B. J. Truhlar, D. G. Development and assessment of a new hybrid density functional model for thermochemical kinetics. J. Phys. Chem. A 2004, 14, 2715-2719. 

Amara, P., Volbeda, A., Fontecilla-Camps, J. C., Field, M. J., 1999, A Hybrid Density Functional Theory/Mo-lecular Mechanics Study of Nickel-Iron Hydrogenase Investigation of the Active Site Redox States , J. Am. Chem. Soc., 121, 4468. 

Barone, V., Adamo, C., Mele, F., 1996, Comparison of Conventional and Hybrid Density Functional Approaches. Cationic Hydrides of First-Row Transition Metals as a Case Study , Chem. Phys. Lett., 249, 290. 

Blomberg, M. R. A., Siegbahn, P. E. M., Svensson, M., 1996, Comparisons of Results From Parameterized Configuration Interaction (PCI-80) and From Hybrid Density Functional Theory With Experiments for First Row Transition Metal Compounds , J. Chem. Phys., 104, 9546. 

Finley, J. W., Stephens, P. J., 1995, Density Functional Theory Calculations of Molecular Structures and Harmonic Vibrational Frequencies Using Hybrid Density Functionals , J. Mol. Struct. (Theochem), 357, 225. 

Halls, M. D., Schlegel, H. B., 1998, Comparison of the Performance of Local, Gradient-Corrected, and Hybrid Density Functional Models in Predicting Infrared Intensities , J. Chem. Phys., 109, 10587. 

Cora F, Alfredsson M, Mallia G, Middlemiss DS, Mackrodt WC, Dovesi R, Orlando R (2004) The Performance of Hybrid Density Functionals in Solid State Chemistry 113 171-232 Cornia A, Costantino AF, Zobbi L, Caneschi A, Gatteschi D, Mannini M, Sessoli R (2006) Preparation of Novel Materials Using SMMs. 122 133-161 Coskun T, see Bouamaied I (2006) 121 1-47 Costantino AF, see Cornia A (2006) 122 133-161... 

However, one feature of the HF potential is that it is not a local potential. In the case of perfect data (i.e. zero experimental error), the fitted orbitals obtained are no longer Kohn-Sham orbitals, as they would have been if a local potential (for example, the local exchange approximation [27]) had been used. Since the fitted orbitals can be described as orbitals which minimise the HF energy and are constrained produce the real density , they are obviously quite closely related to the Kohn-Sham orbitals, which are orbitals which minimise the kinetic energy and produce the real density . In fact, Levy [16] has already considered these kind of orbitals within the context of hybrid density functional theories. 

Neese, F. 2007. Calculation of the zero-field splitting tensor on the basis of hybrid density functional and Hartree-Fock theory. The Journal of Chemical Physics 127 164112/1-9. 

Potassium cation affinities of several azoles and other compounds in the gas phase were calculated by hybrid density functional theory [B3-LYP with 6-311 + G(3df, 2p) basis set] <2003CEJ3383>. There is a striking difference in binding energies of 177- and 277-1,2,3-triazoles. Some of the collected data are as follows ... 

To test the reliability of the B3LYP hybrid density functional, we computed the MP2(full)/6-311+G energies based on the structures obtained at the B3LYP/6-311+G level. The activation barrier at this level is only 12.6 kcal mol-1. This is not... 

The quantum-mechanical energy curve was calculated at the B3LYP/6-311++G level of hybrid density-functional theory, as described in Appendix A. However, due to B3LYP convergence failures beyond Ji 3A, the quantities shown in Figs. 2.4—2.8 were calculated at HF/6-311++G" level. 

Because of the presence of two azide groups in positions adjacent to the ring nitrogen atoms in compound 13a, valence bond isomerization can result in formation of 6-azido-7-methyltetrazolo[l,5-A pyridazine 14a, 6-azido-8-methyltetrazolo[l,5-A pyridazine 15a, and the bis-tetrazole compound 16a. Calculations have been carried out by using hybrid density functional theory (B3LYP/6-311+G(d,p)) and complete basis set treatments (CBS-4M). All calculations revealed that the 8-methyl derivative 15a is the most stable isomer. Similar studies on the triazide derivative 13b, however, indicated that in this case the equilibrium is shifted to the 7-methyl form 14b. All these conclusions proved to be in entire agreement with the experimental findings (see Section 11.18.3.2.). 

The structures of B -Bjj cations shown in Figure 29.1 were taken from the Ref. [7], in which they were considered as the most stable structures previously reported in the literature. They were reoptimized using hybrid density functional method known in the literature as B3LYP [67-69] with the 6-311 +G basis set [70-72] as implemented in Gaussian 03 program [73]. There is no guarantee that all the considered structures here are indeed global minimum structures. 

T. Schwabe and S. Grimme, Double hybrid density functionals with long range dispersion corrections Higher accuracy and extended applicability. Phys. Chem. Chem. Phys. 9, 3397 3406 (2007). 

Regarding the height of the insertion barrier, the situation is much more controversial, since pure density functionals and some MP2 calculations suggest that this a barrierless reaction, or it occurs with a negligible barrier. HF, hybrid density functionals and several post-HF calculations, instead, suggest a barrier in the range of 5-10 kcal/mol, roughly. 

The electronic structure calculations were carried out using the hybrid density functional method B3LYP [15] as implemented in the GAUSSIAN-94 package [16], in conjunction with the Stevens-Basch-Krauss (SBK) [17] effective core potential (ECP) (a relativistic ECP for Zr atom) and the standard 4-31G, CEP-31 and (8s8p6d/4s4p3d) basis sets for the H, (C, P and N), and Zr atoms, respectively. 

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